A uniform rod of mass m is leaning at rest against a smooth wall as shown. Contact force between the rod and the ground is `[cot theta = 2sqrt(3)]`

Options

A. mg
B. `sqrt(3)` mg
C. 2 mg
D. `sqrt(5)` mg

Answer

C

Explanation

`N_(1) = mg`
`f = N_(2)`
for Rotational equilibrium
`rArr |tau_(mg)| = |tau_(N_(2))|`
`rArr mg.l/2 cos theta = N_(2l sin theta`
`rArr N_(2) = (mg.cottheta)/2`
`N_(2) =(mg)/2 xx 2sqrt(3)`
`therefore F_("net") = sqrt((mgsqrt(3))^(2) xx (mg)^(2)) = 2mg`